M1847777 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	16.0809	68.6567%	500000	15000000	0.1015	5.0745%	16.1824	70.2472%	1.5905%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0224%	0.0117	64.2714%	1.1135%
GPU72	2⁶¹	0.1662	65.5738%	9000	150000	0.0013	1.6306%	0.1676	66.1351%	0.5613%
Difference	+6	+15.9147	+3.0829%	+491000	+14850000	+0.1002	+3.4439%	+16.0148	+4.1121%	+4.1121%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0809

68.6567%

500000

15000000

0.1015

5.0745%

16.1824

70.2472%

1.5905%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0224%

0.0117

64.2714%

1.1135%

GPU72

2⁶¹

0.1662

65.5738%

9000

150000

0.0013

1.6306%

0.1676

66.1351%

0.5613%

Difference

+15.9147

+3.0829%

+491000

+14850000

+0.1002

+3.4439%

+16.0148

+4.1121%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1847777	513682007	9	28.936	139 139	-	1	139	1.994e-11	6.701e-7	1.116e-6
1847777	52323590002297	14	45.573	14158524 2² × 3 × 23 × 43 × 1193	2014-01-23	43	1193	4.098e-6	8.311e-6	9.576e-6
1847777	3697363567573310017	19	61.681	1000489660704 2⁵ × 3² × 1013 × 3429341	2015-08-29	1013	3429341	0.2686	0.0148	0.0275
1847777	5200527158851872047	19	62.173	1407238849399 17 × 82778755847	2016-07-06	17	82778755847	0.6245	354.77	662.61
1847777	46594916255753449402151	23	75.303	12608371100991475 5² × 61 × 281887 × 29330137	2020-12-15	281887	29330137	5,212.3	0.1467	0.2348

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1847777

513682007

28.936

139
139

139

1.994e-11

6.701e-7

1.116e-6

1847777

52323590002297

45.573

14158524
2² × 3 × 23 × 43 × 1193

2014-01-23

1193

4.098e-6

8.311e-6

9.576e-6

1847777

3697363567573310017

61.681

1000489660704
2⁵ × 3² × 1013 × 3429341

2015-08-29

1013

3429341

0.2686

0.0148

0.0275

1847777

5200527158851872047

62.173

1407238849399
17 × 82778755847

2016-07-06

82778755847

0.6245

354.77

662.61

1847777

46594916255753449402151

75.303

12608371100991475
5² × 61 × 281887 × 29330137

2020-12-15

281887

29330137

5,212.3

0.1467

0.2348

exponent	prime factors	composite factor	digits	bits*
1847777	513682007 52323590002297	26877686725825057570079	23	74.509
1847777	513682007 3697363567573310017	1899269137999738009165764119	28	90.618
1847777	513682007 5200527158851872047	2671417228417037448810158329	28	91.110
1847777	513682007 46594916255753449402151	23934970098252357186069875797057	32	104.239
1847777	52323590002297 3697363567573310017	193459335399136012387116923109049	33	107.254
1847777	52323590002297 5200527158851872047	272110250855575834603571480091959	33	107.746
1847777	52323590002297 46594916255753449402151	2438013294357407150243359715366740847	37	120.875
1847777	3697363567573310017 5200527158851872047	19228239649314447570173840112747394799	38	123.855
1847777	513682007 52323590002297 3697363567573310017	99376579680714332908991082006320970181343	41	136.190
1847777	513682007 52323590002297 5200527158851872047	139778139784765661859862647261598043681713	42	136.682
1847777	3697363567573310017 46594916255753449402151	172278345798152190184790625257172829646567	42	136.984
1847777	5200527158851872047 46594916255753449402151	242318127452474394058647405586379298573097	42	137.476
1847777	513682007 52323590002297 46594916255753449402151	1252363562138194680253159557012536179335839929	46	149.811
1847777	513682007 3697363567573310017 5200527158851872047	9877200734136821601943171528013188044371681593	46	152.791
1847777	513682007 3697363567573310017 46594916255753449402151	88496286432234833945568949256889430278717637219969	50	165.920
1847777	513682007 5200527158851872047 46594916255753449402151	12447446204226884385615487500695432995428070316567 9	51	166.412
1847777	52323590002297 3697363567573310017 5200527158851872047	10060905278766402022127475248536377697699891758533 03	52	169.427
1847777	52323590002297 3697363567573310017 46594916255753449402151	90142215318164613171293644926544197637825426052281 64399	55	182.556
1847777	52323590002297 5200527158851872047 46594916255753449402151	12678954350947619418981436487618133093658225707052 403809	56	183.048
1847777	513682007 52323590002297 3697363567573310017 5200527158851872047	51681060158336198748952998955109903082645196822060 0622619121	60	198.363
1847777	3697363567573310017 5200527158851872047 46594916255753449402151	89593821620536475836203044026397893308091694479038 9316812649	60	199.157
1847777	513682007 52323590002297 3697363567573310017 46594916255753449402151	46304434080060942050208754312212591016802823970166 12181404268793	64	211.493
1847777	513682007 52323590002297 5200527158851872047 46594916255753449402151	65129507176561554950145581907027132571434763532576 72842781564663	64	211.985
1847777	513682007 3697363567573310017 5200527158851872047 46594916255753449402151	46022734104837169324247782914989430815072410960023 5378571680381306543	69	228.093
1847777	52323590002297 3697363567573310017 5200527158851872047 46594916255753449402151	46878703892118831499607675173849509384449694652551 832775468677350628654753	74	244.730
1847777	513682007 52323590002297 3697363567573310017 5200527158851872047 46594916255753449402151	24080746700862312847213290295907089896569453739659 993131631130547106370085231129271	83	273.666

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-08-29T11:02:00	alpertron	Manual testing	500000	15000000	12		3697363567573310017	19	61.681	0.101	0.200	0.203	5.074%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-08-29T11:02:00

alpertron

Manual testing

500000

15000000

3697363567573310017

61.681

0.101

0.200

0.203

5.074%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-01-23T13:39:00	TJAOI	Manual testing	?	?	52323590002297	45.573	14	1.56153e-6	0.214	3.33690e-6
2016-07-06T14:35:17	TJAOI	Manual testing	2⁶²	2⁶³*	5200527158851872047	62.173	19	0.292	0.204	0.594

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-01-23T13:39:00

TJAOI

Manual testing

52323590002297

45.573

1.56153e-6

0.214

3.33690e-6

2016-07-06T14:35:17

TJAOI

Manual testing

2⁶²

2⁶³*

5200527158851872047

62.173

0.292

0.204

0.594

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.788 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.788 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.631	0.002%
25	50000	0.978	37.591%
30	250000	0.062	93.980%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	2.489
50000	5000000	46594916255753449402151	1	0.069
50000	6600000		221	17.23

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T05:41:36	ATH	ec2-1xe	50000	5000000						3	0.207
2019-01-14T16:33:17	tottenhoff	2013pc	50000	5000000						3	0.207
2020-06-11T01:17:39	kracker	O0	50000	5000000						3	0.207
2020-07-05T20:37:24	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-08-07T08:23:39	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-10-12T19:19:17	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2020-12-15T22:46:29	Poao	virmach-USny	50000	5000000	46594916255753449402151	75.303	1	2	5914000869569971	1	0.069
2021-01-13T02:54:25	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-04-08T04:05:09	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-06-18T16:47:33	TJAOI	Manual testing	50000	6600000						221	17.23